lecture17 - Pythagorean Scale Pythagoras(born about 580 B.C...

Pythagorean ScaleMost consonant intervals:•1:1 – unison•2:1 – octave– 12 semitones •3:2 – perfect 5th– 7 semitones•4:3 – perfect 4th– 5 semitonesPythagoras (born about 580 B.C.)The Pythagorean system is an attempt to build a complete chromatic scale from only two of the pure tones: the octave and the perfect fifth...32243,1681,827,49,23,1...23,23,23,23,23,15432The goal was to close circle (Circle of fifths), i.e. to end up with the same note as started. Unfortunately, it is impossible.;7.1292312≈12827=23423=If octave has 12 semitones, then 7 octaves have 12x7 semitones.If perfect 5thhas 7 semitones, 12 perfect 5thhave 7x12 semitones.

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Questions:•How to construct a convenient scale?•How to set up an interval between notes? What is known:•Perfect fifth plus perfect forth is an octave•Perfect fourth up is the same as octave up and then perfect fifth down•Perfect fifth up is the same as octave up and then perfect fourth down•So we can use octave and perfect fifth to construct perfect fourth•12 perfect 5thare approximately equal to 7 octaves12 semitones! 7 notes!

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